The rectangular base of a box has a perimeter of 60cm. The base is twice as long as it is wide. Saskia plans to cover the top and bottom with coloured paper;which cost 5 cents per square centimetre. She lans to cover the other 4 faces with white paper; which costs 1.5 cents per square centimetre. How much money will Saskia spend to cover the box with paper?(assume there is no waste)
height is 40 cm .
please help
the height is 40 cm
To find out how much money Saskia will spend to cover the box with paper, we first need to calculate the dimensions of the box.
Let's assume the width of the base is "x" cm. Since the base is twice as long as it is wide, the length of the base would be "2x" cm.
The perimeter of a rectangle is given by the formula: P = 2L + 2W, where P represents the perimeter, L represents the length, and W represents the width.
Since the base of the box has a perimeter of 60 cm, we can set up the equation as follows:
60 = 2(2x) + 2x
Simplifying the equation:
60 = 4x + 2x
60 = 6x
Now, we can solve for x:
x = 60 / 6
x = 10
Therefore, the width of the base is 10 cm, and the length is twice the width, which is 20 cm.
The height of the box is given as 40 cm.
Now, let's calculate the areas of each face of the box.
1. The area of each colored top/bottom face:
Since the top/bottom face is a rectangle with sides measuring 20 cm and 10 cm, the area is calculated as:
Area of each colored top/bottom face = length x width
= 20 cm x 10 cm
2. The area of each white face:
There are four white faces in total. Since each face is a rectangle with sides measuring 40 cm (the height) and 10 cm, the area is calculated as:
Area of each white face = height x width
= 40 cm x 10 cm
Now that we have the dimensions and areas, we can calculate the total cost.
1. Cost of covering the top/bottom faces:
The cost for colored paper is 5 cents per square centimeter. So the total cost for the top/bottom faces is:
Cost of covering each colored top/bottom face = Area x Cost per centimeter
= (20 cm x 10 cm) x 5 cents
2. Cost of covering the white faces:
The cost for white paper is 1.5 cents per square centimeter. So the total cost for the white faces is:
Cost of covering each white face = Area x Cost per centimeter
= (40 cm x 10 cm) x 1.5 cents
Now, we can calculate the total cost:
Total cost = (Cost of covering each colored top/bottom face x 2) + (Cost of covering each white face x 4)
Substituting the calculated values:
Total cost = [(20 cm x 10 cm) x 5 cents x 2] + [(40 cm x 10 cm) x 1.5 cents x 4]
Simplifying the equation will give you the final answer, which represents the total cost Saskia will spend to cover the box with paper.